heur_init.h

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/**@file   heur_init.h
 * @brief  initial primal heuristic for the vertex coloring problem
 * @author Gerald Gamrath
 *
 * This file implements a heuristic which computes a starting solution for the coloring problem. It
 * therefore computes maximal stable sets and creates one variable for each set, which is added to the
 * LP.
 *
 * The heuristic is called only one time: before solving the root node.
 *
 * It checks whether a solution-file was read in and there already is a starting solution.  If this
 * is not the case, an initial possible coloring is computed by a greedy method.  After that, a
 * tabu-search is called, which tries to reduce the number of colors needed. The tabu-search algorithm
 * follows the description in
 *
 * "A Survey of Local Search Methods for Graph Coloring"@n
 * by P. Galinier and A. Hertz@n
 * Computers & Operations Research, 33 (2006)
 *
 * The tabu-search works as follows: given the graph and a number of colors it tries to color the
 * nodes of the graph with at most the given number of colors.  It starts with a random coloring. In
 * each iteration, it counts the number of violated edges, that is, edges for which both incident
 * nodes have the same color. It now switches one node to another color in each iteration, taking
 * the node and color, that cause the greatest reduction of the number of violated edges, or if no
 * such combination exists, the node and color that cause the smallest increase of that number.  The
 * former color of the node is forbidden for a couple of iterations in order to give the possibility
 * to leave a local minimum.
 *
 * As long as the tabu-search finds a solution with the given number of colors, this number is reduced
 * by 1 and the tabu-search is called another time. If no coloring was found after a given number
 * of iterations, the tabu-search is stopped and variables for all sets of the last feasible coloring
 * are created and added to the LP (after possible extension to maximal stable sets).
 *
 * The variables of these sets result in a feasible starting solution of the coloring problem.
 *
 * The tabu-search can be deactivated by setting the parameter <heuristics/initcol/usetabu> to
 * FALSE.  The number of iterations after which the tabu-search stops if no solution was yet found
 * can be changed by the param <heuristics/initcol/maxiter>. A great effect is also obtained by
 * changing the parameters <heuristics/initcol/tabubase> and <heuristics/initcol/tabugamma>, which
 * distinguish the number of iterations for which the former color of a node is forbidden; more
 * precisely, this number is <tabubase> + ncritical * <tabugamma>, where ncritical is the number
 * of nodes, which are incident to violated edges.  Finally, the level of output and the frequency of
 * status lines can be changed by <heuristics/initcol/output> and <heuristics/initcol/dispfreq>.
 */
 
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#ifndef __SCIP_HEUR_INIT_H__
#define __SCIP_HEUR_INIT_H__
 
 
#include "scip/scip.h"
 
#ifdef __cplusplus
extern "C" {
#endif
 
/** creates the initial primal heuristic for coloring and includes it in SCIP */
SCIP_RETCODE SCIPincludeHeurInit(
   SCIP*                 scip                /**< SCIP data structure */
   );
 
#ifdef __cplusplus
}
#endif
 
#endif